# Cheapest Superstrategies without the Optional Decomposition

1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : We follow very closely Föllmer and Kabanov Lagrange multiplier approach to superstrategies in perfect incomplete markets, except that we provide a very simple proof of the existence of a minimizing multiplier in case of a European option under the assumption that the discounted process of the underlying is an $L^2\left( P\right)$ martingale for some probability $P.$ Even if it gives the existence of a superstrategy associated to the supremum of the expectations under the equivalent martingale measures, our result is much weaker than the optional decomposition theorem.
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https://hal.inria.fr/inria-00072721
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Submitted on : Wednesday, May 24, 2006 - 10:42:08 AM
Last modification on : Thursday, February 3, 2022 - 11:18:13 AM
Long-term archiving on: : Thursday, March 24, 2011 - 12:13:36 PM

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• HAL Id : inria-00072721, version 1

### Citation

Claude Martini. Cheapest Superstrategies without the Optional Decomposition. [Research Report] RR-3931, INRIA. 2000. ⟨inria-00072721⟩

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